In the realm of laser-plasma interactions, if the laser intensity is strong enough, quantum effects play a significant role. Due to the large separation between the length scale at which quantum electrodynamic processes form and both the typical separation between particles in a plasma and the wavelength of optical lasers, it is possible in many situations of interest to take into account quantum electrodynamic processes in a fairly straightforward way. If one considers plasmas of increasingly large densities, the presence of many particles can render potentially unavoidable a full quantum treatment of the dynamics. Here, two kinds of multi-particle effects are discussed within strong-field Quantum Electrodynamics. First, we show how a correct description of coherence effects in the radiation emitted by a two-electron wave packet in a strong laser field requires a quantum treatment also if the quantum nonlinearity parameter of the system is much smaller than unity. Secondly, we indicate that at solid-state densities the presence of several particles within the formation region of radiation by an electron in a strong electromagnetic field may alter the emission probability itself, such that in general it is not possible to disentangle collective effects from quantum effects.